Oliver was one of Keith Briggs's first signings when he took over. He came through the Everton youth system, before transferring to Watford's youth system. His goal against Leyton Orient for the Youth team was voted goal of the season for the 12/13 season. After Orient, he joined Bacup and Rossendale Borough for a while, before joining Stalybridge Celtic. He won the Young Player of the Year award in 2014. After leaving Celtic, Oliver moved to America in 2015 and played for New Orleans Jesters, before returning in 2017 to play for FC United of Manchester from where he returned to Celtic for a second spell in the 2017/18 season.

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